Fruzsina Mészáros

On Measurable Functions Satisfying Multiplicative Type Functional Equations Almost Everywhere

Using the so-called “almost” variant of a well-known generalization of Steinhaus’ theorem, first we prove a general result on the multiplicative type functional equation (3), then we solve functional equations (1) and (2) originated from statistics under such conditions.

Functional equations stemming from probability theory

Abstract Special cases of the functional equation are investigated for almost all (x, y) ∈ℝ 2+, for the given functions c, d and the unknown functions h1, h2, fX and fY.

Sequenced problems for functional equations

There are many possible methods to solve equations of the form H(f(x + y), f(x − y), f(x), f(y), x, y) = 0 (x, y ∈ R), where H is a known function and f is the unknown function to be determined. Here we will create a sequence of problems for equations of type (1) (see on the next page). These sequenced problems are appropriate for the fostering of talented students on different level of mathematical education.

A Characterization of the Exponential Distribution through Functional Equations

In this paper we give a characterization for the exponential distribution by using functional equations.